Prior to the detailed design of components, turbomachinery engineers must guide a mean-line or throughflow design toward an optimum configuration. This process requires a combination of informed judgement and low-order correlations for the principle sources of loss. With these requirements in mind, this paper examines the impact of key design parameters on endwall loss in turbines, a problem which remains poorly understood. This paper presents a parametric study of linear cascades, which represent a simplified model of real-engine flow. The designs are nominally representative of the low-pressure turbine blades of an aero-engine, with varying flow angles, blade thickness, and suction surface lift styles. Reynolds-averaged Navier–Stokes (RANS) calculations are performed for a single aspect ratio (AR) and constant inlet boundary layer thickness. To characterize the cascades studied, the two-dimensional design space is examined before studying endwall losses in detail. It is demonstrated that endwall loss can be decomposed into two components: one due to the dissipation associated with the endwall boundary layer and another induced by the secondary flows. This secondary-flow-induced loss is found to scale with a measure of streamwise vorticity predicted by classical secondary flow theory.

References

References
1.
Denton
,
J. D.
,
1993
, “
Loss Mechanisms in Turbomachines
,”
ASME J. Turbomach.
,
115
(
4
), pp.
621
656
.
2.
Hawthorne
,
W. R.
,
1955
, “
Rotational Flow Through Cascades—Part 1: The Components of Vorticity
,”
Q. J. Mech. Appl. Math.
,
8
(
3
), pp.
266
279
.
3.
Sieverding
,
C. H.
,
1985
, “
Recent Progress in the Understanding of Basic Aspects of Secondary Flows in Turbine Blade Passages
,”
ASME J. Eng. Gas Turbines Power
,
107
(
2
), pp.
248
257
.
4.
Langston
,
L. S.
,
2001
, “
Secondary Flows in Axial Turbines—A Review
,”
Ann. N. Y. Acad. Sci.
,
934
(
1
), pp.
11
26
.
5.
Adrian
,
R. J.
,
Christensen
,
K. T.
, and
Liu
,
Z.-C.
,
2000
, “
Analysis and Interpretation of Instantaneous Turbulent Velocity Fields
,”
Exp. Fluids
,
29
(
3
), pp.
275
290
.
6.
Denton
,
J. D.
, and
Pullan
,
G. P.
,
2012
, “
A Numerical Investigation Into the Sources of Endwall Loss in Axial Flow Turbines
,”
ASME
Paper No. GT2012-69173.
7.
Pullan
,
G. P.
,
Denton
,
J. D.
, and
Dunkley
,
M.
,
2003
, “
An Experimental and Computational Study of the Formation of a Streamwise Shed Vortex in a Turbine Stage
,”
ASME J. Turbomach.
,
125
(
2
), pp.
291
297
.
8.
Ainley
,
D. G.
, and
Mathieson
,
G. C. R.
,
1957
, “
A Method of Performance Estimation for Axial-Flow Turbines
,”
ARC Reports and Memoranda No. 2974
.
9.
Dunham
,
J.
, and
Came
,
P. M.
,
1970
, “
Improvements to the Ainley–Mathieson Method of Turbine Performance Prediction
,”
ASME J. Eng. Power
,
92
(
3
), pp.
252
256
.
10.
Kacker
,
S. C.
, and
Okapuu
,
U.
,
1982
, “
A Mean Line Performance Method for Axial Flow Turbine Efficiency
,”
ASME J. Eng. Power
,
104
(
1
), pp.
111
119
.
11.
Craig
,
H. R. M.
, and
Cox
,
H. J. A.
,
1971
, “
Performance Estimation of Axial Flow Turbines
,”
Proc. Inst. Mech. Eng.
,
185
(
1
), pp.
407
424
.
12.
Traupel
,
W.
,
1977
,
Thermische Turbomaschinen
,
Springer-Verlag
,
Berlin
.
13.
Benner
,
M. W.
,
Sjolander
,
S. A.
, and
Moustapha
,
S. H.
,
2006
, “
An Empirical Prediction Method for Secondary Losses in Turbines—Part II: A New Secondary Loss Correlation
,”
ASME J. Turbomach.
,
128
(
2
), pp.
281
291
.
14.
Coull
,
J. D.
, and
Hodson
,
H. P.
,
2013
, “
Blade Loading and Its Application in the Mean-Line Design of Low Pressure Turbines
,”
ASME J. Turbomach.
,
135
(
2
), p.
021032
.
15.
Sharma
,
O. P.
, and
Butler
,
T. L.
,
1986
, “
Predictions of Endwall Losses and Secondary Flows in Axial Flow Turbine Cascades
,”
ASME J. Turbomach.
,
109
(2), pp. 229–236.
16.
Drela
,
M.
,
1985
, “
Two-Dimensional Transonic Aerodynamic Design and Analysis Using the Euler Equations
,”
Ph.D. thesis
, Massachusetts Institute of Technology, Cambridge, MA.
17.
Youngren
,
H.
, and
Drela
,
M.
,
1991
, “
Viscous/Inviscid Method for Preliminary Design of Transonic Cascades
,”
AIAA
Paper No. 91-2364.
18.
Coull
,
J. D.
,
Thomas
,
R. L.
, and
Hodson
,
H. P.
,
2010
, “
Velocity Distributions for Low Pressure Turbines
,”
ASME J. Turbomach.
,
132
(
4
), p.
041006
.
19.
Goodhand
,
M. N.
, and
Miller
,
R. J.
,
2011
, “
Compressor Leading Edge Spikes: A New Performance Criterion
,”
ASME J. Turbomach.
,
133
(
2
), p.
021006
.
20.
Howell
,
R. J.
,
Ramesh
,
O. N.
,
Hodson
,
H. P.
,
Harvey
,
N. W.
, and
Schulte
,
V.
,
2001
, “
High Lift and Aft-Loaded Pressure Profiles for Low-Pressure Turbines
,”
ASME J. Turbomach.
,
123
(
2
), pp.
181
188
.
21.
Vázquez
,
R.
,
Torre
,
D.
,
Partida
,
F.
,
Armañanzas
,
L.
, and
Antoranz
,
A.
,
2011
, “
Influence of Surface Roughness on the Profile and End-Wall Losses in Low Pressure Turbines
,”
ASME
Paper No. GT2011-46371.
22.
Shahpar
,
S.
, and
Lapworth
,
L.
,
2003
, “
PADRAM: Parametric Design and Rapid Meshing System for Turbomachinery Optimisation
,”
ASME
Paper No. GT2003-38698.
23.
Moinier
,
P.
, and
Giles
,
M. B.
,
1998
, “
Preconditioned Euler and Navier–Stokes Calculations on Unstructured Grids
,” 6th
ICFD
Conference on Numerical Methods for Fluid Dynamics
, Oxford, UK, Mar. 31–Apr. 3.
24.
Menter
,
F. R.
,
Langtry
,
R. B.
,
Likki
,
S. R.
,
Suzen
,
Y. B.
,
Huang
,
P. G.
, and
Völker
,
S.
,
2006
, “
A Correlation-Based Transition Model Using Local Variables—Part I: Model Formulation
,”
ASME J. Turbomach.
,
128
(
3
), pp.
413
422
.
25.
Halstead
,
D. E.
,
1996
, “
Boundary Layer Development in Multi-Stage Low Pressure Turbines
,”
Ph.D. thesis
, Iowa State University, Ames, IA.
26.
Benner
,
M. W.
,
Sjolander
,
S. A.
, and
Moustapha
,
S. H.
,
2006
, “
An Empirical Prediction Method for Secondary Losses in Turbines—Part I: A New Loss Breakdown Scheme and Penetration Depth Correlation
,”
ASME J. Turbomach.
,
128
(
2
), pp.
273
280
.
27.
Hodson
,
H. P.
, and
Dominy
,
R. G.
,
1987
, “
The Off-Design Performance of a Low-Pressure Turbine Cascade
,”
ASME J. Turbomach.
,
109
(
2
), pp.
201
209
.
28.
Gregory-Smith
,
D. G.
,
Graves
,
C. P.
, and
Walsh
,
J. A.
,
1988
, “
Growth of Secondary Losses and Vorticity in an Axial Turbine Cascade
,”
ASME J. Turbomach.
,
110
(
1
), pp.
1
8
.
29.
Zweifel
,
O.
,
1945
, “
The Spacing of Turbomachine Blading, Especially With Large Angular Deflection
,”
Brown Boveri Rev.
,
32
(12), pp.
436
444
.
30.
Coull
,
J. D.
, and
Hodson
,
H. P.
,
2012
, “
Predicting the Profile Loss of High-Lift Low Pressure Turbines
,”
ASME J. Turbomach.
,
134
(
2
), p.
021002
.
31.
Curtis
,
E. M.
,
Hodson
,
H. P.
,
Banieghbal
,
M. R.
,
Denton
,
J. D.
,
Howell
,
R. J.
, and
Harvey
,
N. W.
,
1997
, “
Development of Blade Profiles for Low-Pressure Turbine Applications
,”
ASME J. Turbomach.
,
119
(
3
), pp.
531
538
.
32.
Zhou
,
C.
,
Hodson
,
H. P.
, and
Himmel
,
C.
,
2014
, “
The Effects of Trailing Edge Thickness on the Losses of Ultra-High Lift LP Turbine Blades
,”
ASME J. Turbomach.
,
136
(
8
), p.
081011
.
33.
Michelassi
,
V.
,
Chen
,
L. W.
,
Pichler
,
R.
, and
Sandberg
,
R. D.
,
2015
, “
Compressible Direct Numerical Simulation of Low-Pressure Turbines—Part II: Effect of Inflow Disturbances
,”
ASME J. Turbomach.
,
137
(
7
), p.
071005
.
34.
Squire
,
H. B.
, and
Winter
,
K. G.
,
1951
, “
The Secondary Flow in a Cascade of Airfoils in a Nonuniform Stream
,”
J. Aeronaut. Sci.
,
18
(
4
), pp.
271
277
.
35.
Marsh
,
H.
,
1976
, “
Secondary Flow in Cascades—The Effect of Compressibility
,”
Aeronautical Research Council R&M No. 3778
.
36.
Came
,
P. M.
, and
Marsh
,
H.
,
1974
, “
Secondary Flow in Cascades: Two Simple Derivations for the Components of Vorticity
,”
J. Mech. Eng. Sci.
,
16
(
6
), pp.
391
401
.
37.
Hodson
,
H. P.
,
2012
, “
Blade to Blade Flowfields in Axial Turbomachines
,”
Cambridge Turbomachinery Course 2012
, Vol.
1
, University of Cambridge, Cambridge, UK, pp.
35
75
.
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